Given the mass of a star, determine Kepler's constant.

[Solidearth]

Homework Statement

"The mass of a star is 4.85x10^29kg. In scientific notation, Kepler's constant for that star is bx10^w s²/m³. the value of b is_____."

Homework Equations

K=T²/r³

The Attempt at a Solution

This problem is very tough. I first assumed that K would be 0 because the star has no satellites, and therefore is experiencing linear motion, not circular motion. To my dismay however, the answer is indeed 3 digits and K_star> 0.
The greatest obstacle is how am I to derive the period and semi major axis of its orbit, if i am only given the star's mass?!
Any insights into this problem are helpful.
Thanks!

 

[LowlyPion]

Homework Statement

"The mass of a star is 4.85x10^29kg. In scientific notation, Kepler's constant for that star is bx10^w s²/m³. the value of b is_____."

Homework Equations

K=T²/r³

The Attempt at a Solution

This problem is very tough. I first assumed that K would be 0 because the star has no satellites, and therefore is experiencing linear motion, not circular motion. To my dismay however, the answer is indeed 3 digits and K_star> 0.
The greatest obstacle is how am I to derive the period and semi major axis of its orbit, if i am only given the star's mass?!
Any insights into this problem are helpful.
Thanks!

Welcome to PF.

If K = T²/ a³

Can't you determine K directly from:

T = 2π*(a³/GM)^1/2

Yielding

K = 4π²/(G*M)